An open source software package for primality testing of numbers of the form p2^n+1, with no constraints on the relative sizes of p and 2^n
- Published
- Accepted
- Subject Areas
- Cryptography, Data Science, Theory and Formal Methods
- Keywords
- software, prime, encryption, proth, sierpinski, repeated squaring, multithreading
- Copyright
- © 2018 Rao
- Licence
- This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, reproduction and adaptation in any medium and for any purpose provided that it is properly attributed. For attribution, the original author(s), title, publication source (PeerJ Preprints) and either DOI or URL of the article must be cited.
- Cite this article
- 2018. An open source software package for primality testing of numbers of the form p2^n+1, with no constraints on the relative sizes of p and 2^n. PeerJ Preprints 6:e27396v1 https://doi.org/10.7287/peerj.preprints.27396v1
Abstract
We develop an efficient software package to test for the primality of p2^n+1, p prime and p>2^n. This aids in the determination of large, non-Sierpinski numbers p, for prime p, and in cryptography. It furthermore uniquely allows for the computation of the smallest n such that p2^n+1 is prime when p is large. We compute primes of this form for the first one million primes p and find four primes of the form above 1000 digits. The software may also be used to test whether p2^n+1 divides a generalized fermat number base 3.
Author Comment
This is a submission to PeerJ Computer Science for review.
Supplemental Information
Table of primover p2^n+1, p>2^n, for first million primes p
The left column lists the input values p whereas the right column gives all corresponding n such that p2^n+1 is primover for p>2^n. Furthermore, each result is in fact prime as it does not divide a generalized Fermat number base 3.